Advances in the Spatial Equilibrium Modeling of Mineral and Energy Issues

Abstract

Spatial equilibrium programming methods are increasingly being applied to modeling regional mineral and energy issues. Spatial equilibrium models have been developed to analyze regional commodity trade problems in a national and international context. Mineral models deal with nonfuel minerals and energy models with fuel minerals. Recent modeling efforts focus on conventional fuel and nonfuel mineral trade problems, recognizing the importance of transport costs and political constraints in formulating an equilibrium that approximates competitive trade. Other recent efforts focus on the engineering processes required to transform primary mineral ores or fuels to their more useful processed stages. This paper reviews the theoretical approaches of spatial equilibrium models, compares them to other methods, introduces new modeling advances, and provides a perspective on future modeling directions.

Environment and trade: a review of issues and methods

“…The spatial nature of economic activities and variables was first put into examination in the early 1950s and spatial equilibrium analysis featured the literature of that time (Enke 1951 andSamuelson 1952). Since the 1960s, spatial analysis in economics has greatly expanded its range of study, varying from spatial equilibrium models for trade, transportation and labor markets, to various kinds of more general models for environmental, energy, and geographical and regional economic analyses, e.g., see Labys, Takayama and Uri (1989), Labys and Yang (1991), van den Bergh, Nijkamp and Rietveld (1996), Nijkamp (1986), and Bockstael (1996).…”

Modeling the international competitiveness of Botswana's coal

“…In the regional models, the demand for coal is estimated from two step models of energy demand in which the first step is to estimate the total regional energy for residential and commercial users on the one hand and industrial users on the other and secondly, to employ a conditional logit model for the choice of fuels to meet the estimated energy demands (Baughman, Joskow and Kamat, 1979). In the non-linear regional trade models with both elastic supply and demand functions included in the model, the estimation of the supply and demand equations invokes the regional market equilibrium conditions that supply should equal to demand (see Labys and Yang, 1980). The objective function for the spatial and dynamic optimization model for this study consists of four terms: capital expenditure costs, rail transportation costs, maritime transportation costs and variable supply costs.…”

“…We apply microeconomic theory in the specification of the derived demand for steam coal for electricity generation and, therefore, take into account substitution effects among the fossil fuels for electricity generation. While existing regional studies that have employed econometrically estimated supply functions (Yang, Hwang and Sohng, 2002, Yang and Labys, 1991, these have tended to concentrate on the short run marginal supply functions as opposed to those for the long run. In this study, we estimate the long run marginal cost functions for the net exporting countries within the model and these are then used in the spatial and dynamic optimization model both to simulate and to forecast the temporal and spatial distribution of the seaborne steam coal trade.…”

“…Spatial price equilibrium models have found plenty of application in models to explain the pattern in both the regional and international trade in mineral, energy and agricultural commodities (see van den Bergh, Nijkamp and Rietveld, 1995, Labys, Takayama and Uri, 1991, Labys and Yang, 1991, for a review of mineral and energy models; and Koo and Larson (1985) for a review of agriculture models). This review covers linear programming, quadratic programming, which is a type of non-linear programming, variational inequality and mixed integer programming, which can be linear or non-linear.…”

“…The modern formulation of the spatial price equilibrium model, as a maximization problem, is attributed to Samuelson (see Takayama and Judge, 1964, Florian and Los, 1982, Nagurney, 1987and Labys and Yang, 1991. Takayama and Judge (1964) converted the Samuelson-Enke problem into a quadratic programming problem by making assumptions of linear regional supply and demand functions.…”